What is the Greatest Common Factor of 17889 and 17904?

Greatest common factor (GCF) of 17889 and 17904 is 3.

GCF(17889,17904) = 3

We will now calculate the prime factors of 17889 and 17904, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17889 and 17904.

How to find the GCF of 17889 and 17904?

We will first find the prime factorization of 17889 and 17904. After we will calculate the factors of 17889 and 17904 and find the biggest common factor number .

Step-1: Prime Factorization of 17889

Prime factors of 17889 are 3, 67, 89. Prime factorization of 17889 in exponential form is:

17889 = 3¹ × 67¹ × 89¹

Step-2: Prime Factorization of 17904

Prime factors of 17904 are 2, 3, 373. Prime factorization of 17904 in exponential form is:

17904 = 2⁴ × 3¹ × 373¹

Step-3: Factors of 17889

List of positive integer factors of 17889 that divides 17889 without a remainder.

1, 3, 67, 89, 201, 267, 5963

Step-4: Factors of 17904

List of positive integer factors of 17904 that divides 17889 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 373, 746, 1119, 1492, 2238, 2984, 4476, 5968, 8952

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17889 and 17904. The biggest common factor number is the GCF number.
So the greatest common factor 17889 and 17904 is 3.

Also check out the Least Common Multiple of 17889 and 17904